Variable Priority for Unsupervised Variable Selection

In unsupervised settings where labeled data is unavailable, identifying informative features is both challenging and essential. Although numerous methods for unsupervised feature selection have been proposed, significant opportunities for improvement remain. This paper introduces a new method that extends the supervised Variable Priority (VarPro) framework to the unsupervised domain. The central idea is to recast feature selection as a collection of localized two-class classification problems, where class labels are defined by membership in regions derived using decision tree rules and their corresponding releases. This transformation introduces a form of implicit supervision without requiring outcome labels and is combined with lasso-based regression to encourage sparsity and mitigate noise in high-dimensional settings. Extensive experiments on synthetic benchmarks demonstrate consistent improvements over existing methods across a range of latent, correlated, and clustered scenarios. Real-world validation in biological and image data further confirms the method's effectiveness, including recovery of known cancer-associated genes and improved clustering in lung cancer subtyping.